I think I just became a QBist ?

[strangerep]

Not sure whether it works in this case, but if there are two calibrations, and they are not consistent, maybe we could test the "perception". Suppose the sensory input is 1 and 0, and I perceive it as A and B while you perceive it as B and A, and for the purpose of the logic we agree on everything, ie. we agree 1 is "A" and 0 is "B". But if there is a part of the brain that likes A and hates B, and if this part is the same in you and me, then when we see 1, I will like the input and you will hate it. If we switch the part of the brain that does the liking, then I will hate 1 and you will like it. Then we will have some evidence that we don't see 1 and 0 the same, but we both like A and hate B the same. [...]

I'm not really sure what your point is here.

I usually think we do remember the future - it's called prediction.

That's an... "interesting" redefinition of English words.

I would have said we "speculate" about the future (though sometimes "speculate" and "remember" get mixed up, such as when dreaming, or during a state of delirium).

However, because entropy increases with time, we remember the future less than the past.

Then why do I jump out of my skin when an unexpected loud noise occurs nearby? Entropy surely didn't increase so much that I would totally "forget" that such a significant event is about to happen in my immediate future...

 

[strangerep]

[...]
It doesn't need to be "the same". The description of it only needs to be covariant (in a generalized sense -- my frequency perception spectrum must be consistently calibratable against yours, so that we can agree whether something is/isn't "blue").

Atyy,

Your previous reply prompted a followup thought that different observers also need to share a set of observables, presumably organized as a Lie algebra, so that they are working with a common set of types. But... then there are other issues: the algebras could appear different, while nevertheless being isomorphic.

 

[Paulibus]

The description which physicists give of Nature, however mathematically sophisticated it is, includes certain elements which appear the same to all observers, namely constants like c and h.

These seem to me to be discovered aspects of nature, parts of discovered reality that emerge from the consensual but invented language of mathematics used by physicists to describe this reality with S.I. units.

As Audioloop commented in #52 --- perhaps too simplistically --- "... NATURE is more than equations".

 

[atyy]

I'm not really sure what your point is here.

Your previous reply prompted a followup thought that different observers also need to share a set of observables, presumably organized as a Lie algebra, so that they are working with a common set of types. But... then there are other issues: the algebras could appear different, while nevertheless being isomorphic.

My point is I think Mermin is using the wrong Einstein theory of relativity. He should use - not sure if this is apocryphal or not -this Einstein theory of relativity: ""When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute and it's longer than any hour. That's relativity.""

That's an... "interesting" redefinition of English words.

I would have said we "speculate" about the future (though sometimes "speculate" and "remember" get mixed up, such as when dreaming, or during a state of delirium).

Then why do I jump out of my skin when an unexpected loud noise occurs nearby? Entropy surely didn't increase so much that I would totally "forget" that such a significant event is about to happen in my immediate future...

Because thermodynamics is not the full answer. Psychological time is not the same as a thermodynamic time, although I believe the thermodynamic arrow is part of the answer for why we experience a flow of time. I like Demystifier's essay on this very much. If I understand corectly, Rovelli implicitly advocates a similar point of view in his book on quantum gravity. If this point of view is correct, then Mermin is not even understanding the question. It's like using decoherence to solve the measurement problem.

Your previous reply prompted a followup thought that different observers also need to share a set of observables, presumably organized as a Lie algebra, so that they are working with a common set of types. But... then there are other issues: the algebras could appear different, while nevertheless being isomorphic.

This is a bit tangential to the above thought, but anyway, it seems to be along "operational" lines, so I thought I'd share another BTSM paper that takes on "operational point of view", written by Schroedinger's Rat and Harald Wunderlich: http://arxiv.org/abs/0907.0372

 

[marcus]

Smerlak and Rovelli criticize the notion of a classical observer. Is it fair, however, to say that RQM assumes a classical spacetime?

This question ...made me remember a few other papers which may be pieces of the puzzle…

==quote Strangerep post #32==

They've been discussed here on BTSM in the past, but here are the main references...

----------------------------
S. Gielen, D. Wise, "Lifting General Relativity to Observer Space",
J. Math. Phys. 54, 052501 (2013), http://arxiv.org/abs/1210.0019

Abstract:
The `observer space' of a Lorentzian spacetime is the space of future-timelike unit tangent vectors. Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract observer space geometries for which no underlying spacetime is assumed. We propose taking observer space as fundamental in general relativity, and prove integrability conditions under which spacetime can be reconstructed as a quotient of observer space. Additional field equations on observer space then descend to Einstein's equations on the reconstructed spacetime. We also consider the case where no such reconstruction is possible, and spacetime becomes an observer-dependent, relative concept. Finally, we discuss applications of observer space, including a geometric link between covariant and canonical approaches to gravity.
------------------------
(My emboldening.)

(See also the references therein to their earlier work. The basic idea is to start from a nonholonomic field of observers (meaning a nonintegrable field of tetrad reference frames, iiuc).

Gielen & Wise cite the following paper (also discussed here before, iirc):

G. Amelino-Camelia, L.tFreidel, J. Kowalski-Glikman, L. Smolin,
"The principle of relative locality",
http://arxiv.org/abs/1101.0931

Abstract:
We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them.
This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.
==endquote==

I think Strangerep is setting out some diverse researches that COULD be seen as signs of a novel form of REALISM or a new ontology. In this novel perspective there is a single reality which we can all see and about which we communicate and try to arrive at common understanding. But the novelty is that the various observers cannot construct a single overarching 4D continuum. There is no one spacetime that they have in common.

So Atyy's question about whether one of the approaches assumes a classical spacetime points to a key issue.

 

[Demystifier]

...but NATURE is more than equations.
.

It certainly is, but that constatation alone cannot resolve any problem one might have with the equations. Perhaps it can give someone a reason not to search for a resolution, but a reason not to search for a resolution is not a resolution.

 

[marcus]

...I think all this can be reduced to the following question:
Who is more clever, the physics equations, or the physicists who invented them?

If physicists are more clever, and equations merely represent a part of all things which they understand, then Mermin is right: Equations are nothing but a part of our description of our knowledge about the world, not the reality. If so, then there is no problem of now, no problem of interpretation of quantum mechanics, etc.

However, there are good reasons to believe that equations are more clever than the physicists who invented them...

...but NATURE is more than equations.

I don't see Nature as "more than", I see it as DISJOINT from the human description. Let's not confuse the description with the reality. This "clever equations" talk verges on superstition or mysticism. AFAIK math is an artificial human-invented language. The meaning of an equation can change as the variables get redefined. Equations have limited applicability and sometimes get discarded and replaced by improved equations which again have limited applicability and are subject to eventual improvement.

It certainly is, but that constatation alone cannot resolve any problem one might have with the equations. Perhaps it can give someone a reason not to search for a resolution, but a reason not to search for a resolution is not a resolution.

Demy, what can you mean by "search for a resolution"? One searches for improved understanding, a simpler better-fitting model, more precise reliable prediction. Do you imagine that there is some final "ontology"? A final equation that will tell us what Nature "IS"?

 

[marcus]

By pointing to the Gielen Wise paper, Strangerep raises the possibility that a next-generation REALIST description of the world could enjoy the feature that no reconstruction of spacetime is possible. The math description could describe an objective reality shared by all observers, but as a minor detail that description would contain no consensus continuum.

So? Big deal we would still be assuming an objective reality shared by all observers. But with the proviso that each observer has to construct an imagined 4D continuum for hermself. If that seems funny it is only because we have an engrained habit of presuming that any math description of objective common reality MUST include a 4D continuum. It is admittedly a widespread prejudice.

 

[marcus]

I see Strangerep already suggested "Maybe…" what I just now said. "The notion of a physically-real global spacetime manifold is so deeply entrenched." There's the rub. People naively confuse discarding that entrenched notion with "Solipsism". It's not. It's just a new line of mathematical investigation e.g. by such as Laurent Freidel and Derek Wise.

==Quote by atyy==
[...] If what [Mermin] is saying is just common sense (and it seems to be), why does he write it as if it's such a big deal?
===
Maybe because the notion of a physically-real global spacetime manifold is so deeply entrenched, yet easily questioned by pointing out that each of us only synthesize it based on received stimuli.

==Quote by atyy==
There is one part where I think I definitely disagree with him. Isn't the perception of "now" part of the "hard problem" of consciousness? Like is the "blue" I see the same as the "blue" you see?
===
It doesn't need to be "the same". The description of it only needs to be covariant (in a generalized sense -- my frequency perception spectrum must be consistently calibratable against yours, so that we can agree whether something is/isn't "blue").

Strangerep, This post reminds me of the C*algebra representation of reality used in several recent papers by Carlo Rovelli. There is no "spacetime" continuum but there is an algebra of observables, and there is a physical state which is a positive functional defined on that C* algebra.

Atyy,
Your previous reply prompted a followup thought that different observers also need to share a set of observables, presumably organized as a Lie algebra, so that they are working with a common set of types. But... then there are other issues: the algebras could appear different, while nevertheless being isomorphic.

In that particular treatment the existence of a physical state (not a hilbertspace vector, but a positive functional that assigns expectation values to observables) can be used to generate a global semigroup flow among the observables ("Tomita time"). So it has some parallels with what you mentioned.

 

[atyy]

marcus, I think you once said the one concern you had with the general boundary formalism is that it seems that one could not do quantum cosmology with it. But if one buys that one can at present apply the Copenhagen interpretation (by which I just mean shut-up-and-calculate) with a Heisenberg cut between the quantum and classical to eg. CMB aniostropies, then it seems that in principle the general boundary formalism might still allow us to answer in principle things like the resolution of the big bang singularity that I think you classify as part of quantum cosmology. Here my approach is yes there is an underlying reality (which is a yet unknown but useful model), and quantum mechanics is an "operational" theory in the sense that it requires two realities (classical and quantum) for us to use it, whereas a "reality based" model would have only one "reality". Would this work for you?

BTW, as a biologist, I can tell you everyone assumes their model is wrong, but hopefully it is useful. So it will be a big surprise to me if physicists are more naive than biologists. I'd imagine the difference between biologists and physicists is that physicists are more likely to suspect that any model will be incomplete in principle. In fact, I can claim it is textbook physics http://dao.mit.edu/~wen/book/preintro.pdf: "The physical theory that can be formulated cannot be the final ultimate theory. The classification that can be implemented cannot classify everything. The unformulatable ultimate theory does exist and governs the creation of the universe. The formulated theories describe the matter we see everyday."

BTW #2, I am still extremely befuddled by what Dittrich is doing with the general boundary formalism, even after seeing her Perimeter talk which you helpfully posted in some other thread ...

 

[atyy]

B Red:NOT mere description. That is what I'm taking issue with in the post (not with your comment particularly, I would just put it more strongly)

I don't think this word choice really matters. I think one can rephrase the question in this way to see why QBism seems different. If we have a theory of "physics", then shouldn't that theory include my perceptions? In textbook quantum physics, we always divide the world into classical and quantum, and we have to have the collapse of the wave function. Since my perception is classical and continuous, it doesn't seem to be explained by the textbook interpretation of quantum physics. If it is not explained, shouldn't I look for a theory that explains my perceptions? If we take the Bohmian interpretation or many-worlds (not sure it works, but I'll say the solutions out there are pretty convincing), the problem is solved. QBism seems to deny there's even a problem. Of course this not the full solution - just like the second law is not the full solution as to why we remember the past but don't know the future as well, but it seems to be part of the solution.

Again, in classical physics, we can feel sensations like pain. We think a rock doesn't feel pain, but we imagine that a cockroach might. Can we have a theory that tells us which things feel pain? Mermin's CBism seems completely off the mark. As I said above, I think Mermin is using the wrong Einstein theory of relativity. He should use - not sure if this is apocryphal or not -this Einstein theory of relativity: "When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute and it's longer than any hour. That's relativity."

Basically, QBism seems to deny the "measurement problem", while Mermin seems to deny or have claimed to have solved the "hard problem of consciousness". I'll agree that the latter is less agreed on as a problem than the former - Dennett, for example, seems to believe the "hard problem" does not exist. Here is one description of the "hard problem of consciousness" by Ramachandran, at about 1:00 of http://www.theemotionmachine.com/dr-ramachandran-discusses-consciousness-qualia-and-self (he uses the word "solipsistic" at 2:57).

 

[strangerep]

The description which physicists give of Nature, however mathematically sophisticated it is, includes certain elements which appear the same to all observers, namely constants like c and h.

Well, they only have the same values for all observers if those observers share a common set of reference scales.

However, they do appear as dimensionful constants in the Lie algebra of observables (quantities), and it appears that the experiences of all observers may be organized into a common Lie algebra of quantities, and/or possibly an integration of such quantities, e.g., to a dynamical (semi)group.

As Audioloop commented in #52 --- perhaps too simplistically --- "... NATURE is more than equations".

But I wonder... is nature more than (isomorphic with) the maximal set of solutions of some set of equations? This is unclear to me, since although only some of the solutions are obvious representations of some natural scenario, we don't necessarily see all the solutions unless we can somehow physically implement the full (semi)group of motions on the dynamical phase space.

 

[strangerep]

[...] Psychological time is not the same as a thermodynamic time, [...]

I take your point about "psychological time" -- though it discourages me deeply.

Then... mixing the contexts of (our limited understanding of) psychological time, and Quantum Bayesianism... ...
I begin to feel like Winny the Pooh (a bear of little brain)...

I like Demystifier's essay on this very much.

The distinction between psychological time and parameter time is indeed important to point out.
(However, omitting the speculations near the end about "unmatter" would improve the essay, imho.)

 

[strangerep]

[...] "The notion of a physically-real global spacetime manifold is so deeply entrenched." There's the rub. People naively confuse discarding that entrenched notion with "Solipsism". It's not. It's just a new line of mathematical investigation e.g. by such as Laurent Freidel and Derek Wise.

Yes, thank you. I was trying to think of a polite way to phrase a similar objection. (I had got the feeling that if one rejects the dogma of a "God-view" type of reality, then one is immediately branded a solipsist. )

[...] This post reminds me of the C*algebra representation of reality used in several recent papers by Carlo Rovelli. There is no "spacetime" continuum but there is an algebra of observables, and there is a physical state which is a positive functional defined on that C* algebra.
In that particular treatment the existence of a physical state (not a hilbertspace vector, but a positive functional that assigns expectation values to observables) can be used to generate a global semigroup flow among the observables ("Tomita time"). So it has some parallels with what you mentioned.

I recall trying to read some of that stuff (though I think I might have seen "Tomita time" in the context of one of Bert Schroer's for-me-incomprehensible papers). I must admit I failed to understand Rovelli's C* algebra stuff easily when it appeared on the arxiv.

Therefore, I should try again... harder. Could you remind me of the most relevant reference(s), pls?

 

[atyy]

I recall trying to read some of that stuff (though I think I might have seen "Tomita time" in the context of one of Bert Schroer's for-me-incomprehensible papers). I must admit I failed to understand Rovelli's C* algebra stuff easily when it appeared on the arxiv.

Were you referring to Tomita time when you said time is a semigroup? I don't understand the algebraic part of it, but Tomita time features in quantum gravity. A simple version of the idea is that in Minkowski spacetime, if you take the half space at a fixed time, its causal development is the Rindler wedge. The reduced density matrix of the half space is thermal with respect to the Hamiltonian of a Rindler observer, which provides intuition why the Rindler observer sees thermal Unruh radiation. The Rindler Hamiltonian generates "time" for a Rindler observer, which is why Rovelli called it thermal time. It also goes by the name of Tomita-Takesaki flow or modular flow. The role in quantum gravity, apart from Rovelli's intuition, comes about because of the gauge/gravity conjecture of string theory, in which a QFT in d+1 dimensions is a theory of gravity in d+2. Not sure I got that right, but a reference which uses more easy for me to understand language is http://arxiv.org/abs/1109.1283 (see the right column on p2).

The modular Hamiltonian plays a part in the derivation (using other conjectures) of the linearized Einstein equations in http://arxiv.org/abs/1312.7856 .

 

[Paulibus]

I like it because (imho) it {C.A.Fuchs, N.D.Mermin, R.Schack, "An Introduction to QBism with an Application to the Locality of Quantum Mechanics", http://arxiv.org/abs/1311.5253} cuts through a lot of the widespread BS that wafts around QM.

Me too. Coming back to the nuts and bolts of physical constants whose values are agreed upon as
part of consensual reality, say h and c: It would be interesting to know whether the Qbist approach to Quantum Mechanics could throw any light on what I find mysterious; why the quantum domain is, for us, so very, very local. I fear that the answer may be: just happenstance, part of our contingent circumstances; like the extreme speed of light?

We invent math metaphors to organize our accumulated knowledge and to predict about future knowledge...don't confuse the metaphor with the reality.

Yes, I agree strongly.

An example in Quantum Mechanics may be the wave/particle duality; where our mathematical description of Nature on a certain scale involves probability waves that can also masquerade as particles. This is convenient; I think because the probability of an action having a particular outcome is just the one’s complement of it not having this outcome, rather as a wave’s peak can cancel another’s trough. This is a convenient matching of description to perceived reality, rather than something of deep physical significance?

 

[Paulibus]

P.S. Unsurprisingly, I'm all in favour of what Fuchs has called a 'Paulian idea'. Particularly when it is boosted from lovely Stellenbosch.

 

[strangerep]

Were you referring to Tomita time when you said time [evolution] is a semigroup?

No, but thanks for your brief summary.

I need to catch up on all the various links that you and others have mentioned in this thread before I try to continue...

 

[marcus]

... Could you remind me of the most relevant reference(s), pls?

I'm actually not sure which, if any, are relevant, and can't say which are most relevant. I really like this thread as it is is going, especially your intuition that there can be a common reality we all experience and get our measurements from but that does NOT have to involve a unique official representation of global spacetime (there's only an entrenched habit of expecting that.)

From the standpoint of growing that rather beautiful, slightly astonishing idea it may be a mistake to venture into C* algebra too far or work too hard on anyone implementation. You already have Freidel "relative locality" and Wise "observer space", maybe that is enough for the idea to germinate with.

Since you ask for some references though, I'll give some links (definitely as a non-expert)
https://www.physicsforums.com/showthread.php?p=4214991#post4214991

That is post #21 of a thread I started about Tomita time in the C* formulation of a quantum theory. Post #20 had a rough summary overview without links, and #21 followed with some links. I also redid the summary later in post #37 of the same thread, which was of uneven quality.

A central paper, for me, that got me interested in the thermal time (Tomita time) idea was this
http://arxiv.org/abs/1209.0065
General relativistic statistical mechanics
Carlo Rovelli
(Submitted on 1 Sep 2012 (v1), last revised 19 Nov 2012 (this version, v2))
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = hbar d tau/ds, with k the Boltzmann constant, hbar the Planck constant, ds proper time and d tau the equilibrium thermal time.
Comments: A tentative second step in the thermal time direction, 10 years after the paper with Connes. The aim is the full thermodynamics of gravity. The language of the paper is a bit technical: look at the Appendix first (expanded in version 2)

 

[strangerep]

Coming back to the nuts and bolts of physical constants whose values are agreed upon as part of consensual reality, say h and c: It would be interesting to know whether the Qbist approach to Quantum Mechanics could throw any light on what I find mysterious; why the quantum domain is, for us, so very, very local. I fear that the answer may be: just happenstance, part of our contingent circumstances; like the extreme speed of light?

I'm inclined to say "yes, it's inevitable happenstance".

The so-called "classical limit" corresponds to circumstances where the system action is large compared to $\hbar$. Moreover, it also corresponds to the "large-N" limit, where N is the number of elementary components of a composite system.

 

[strangerep]

[...] it may be a mistake to venture into C* algebra too far

I think about this in the context of the question (borrowing part of your phrase): "what is the mathematical content of the principle that the laws of physics are the same for all observers, if there is no unique official representation of global spacetime ? "

 

[marcus]

I guess the good (and also the bad) thing about the C* embodiment of this idea is that it backs away the idea of a global geometry and focuses entirely on the algebra of observables. It focuses on actual measurements.

I believe it was von Neumann who observed that you can formulate QM without a Hilbert space of states. If you HAD a Hilbert space you could take the "von Neumann" algebra of observables on it and then pick one state, and throw away the rest of the Hilbert space. That chosen state provides a positive linear functional on the algebra (expectation value of the observable evaluated on that state).

So now you have an abstract algebra (which happens to have an adjoint or * operation) and a positive functional on it.

That is just as good a place to start a quantum theory as the conventional Hilberspace is. And there is a Gelfand NaimarkSegal construction that recovers an equivalent Hilbertspace. So it seems like nothing has changed it is all pure mathematical fiddlesticks.

But starting with a C* algebra with a positive functional (a "state") defined on it nevertheless proved to be a fertile new approach.

One odd advantage: in usual QG there's no preferred idea of time BUT R. thinks that to do thermodynamics and to do statistical mechanics you NEED a global time at least as an occasional point of reference HOWEVER in the C* formulation something like a global time emerges from the positive linear functional called the STATE. It also uses the adjoint or * that comes with the abstract algebra.

 

[marcus]

I think about this in the context of the question (borrowing part of your phrase): "what is the mathematical content of the principle that the laws of physics are the same for all observers, if there is no unique official representation of global spacetime ? "

You know more and think deeper than I do. I'm interested to see how this thread goes. Right now I have to go for a walk up this grassy tree grown hill near the house, , it overlooks the Bay. It is 5:03PM Pacific time and getting dark already. If I don't go I get more like a vegetable. Back later

 

[strangerep]

You know more and think deeper than I do.

Rubbish.

Depending on how the "algebra of observables" sub-theme of this thread develops, I might get to prove that it's rubbish.

 

[Demystifier]

Demy, what can you mean by "search for a resolution"?

Searching for a new description, new equations, which better fits nature as we see it.

 

[marcus]

Searching for a new description, new equations, which better fits nature as we see it.

It sounds like what you had in mind, then, was not a final theory but an incremental improvement.
Thanks for the clarification.

Quote by audioloop
...but NATURE is more than equations.

It certainly is, but that constatation alone cannot resolve any problem one might have with the equations. Perhaps it can give someone a reason not to search for a resolution, but a reason not to search for a resolution is not a resolution.

As an experiment, let me try this substitution using what you say you meant by "resolution":
Perhaps it can give someone a reason not to search for a better fit, but a reason not to search for a better fit is not a better fit.

I was puzzled by this exchange. I assume that equations are just description in an evolving artificial human language which hopefully will get better over time (if people keep trying). And I assume that as such the equations are DISJOINT from the reality. Nature is not merely "more" but actually other than our current most reliable description---reality is not to be confused with the description.

I do not see how this could be imagined to be a reason to stop trying to find a better description. AFAICS there is no reason not to keep striving for simpler/more reliable/more accurate/more beautiful models.

So I did not understand what you said about "Perhaps it can give someone a reason not to search for a resolution…"

If you simply mean incrementally improved accuracy etc then how could what Audioloop said give someone a reason not to improve the description?

Also it seemed to me that in your post you were hinting at some mysterious "ontological" connection between our human equations and the reality: that the description really was connected somehow with true Being---that the equations "knew more" than we do.

Let me also say a few words on the Mermin's essay.

I think all this can be reduced to the following question:
Who is more clever, the physics equations, or the physicists who invented them?

If physicists are more clever, and equations merely represent a part of all things which they understand, then Mermin is right: Equations are nothing but a part of our description of our knowledge about the world, not the reality. If so, then there is no problem of now, no problem of interpretation of quantum mechanics, etc.

However, there are good reasons to believe that equations are more clever than the physicists who invented them. In other words, equations know a lot which their inventers do not. For example, Dirac new nothing about positrons when invented the Dirac equation, and the inventers of quantum electrodynamics new nothing about 10 digits of the quantity g-2.

So, as equations seem to know more than their inventors, it is hard not to take the equations seriously and believe that they represent something more than merely our current incomplete knowledge about the world. Of course, with such an attitude, there is a problem of now and there is a problem of interpretation of quantum mechanics, because the equations we currently know do not provide a direct answer.

 

[atyy]

Another paper with comments on what might be beyond quantum theory.

http://arxiv.org/abs/quant-ph/0102043
Causal and localizable quantum operations
David Beckman, Daniel Gottesman, M. A. Nielsen, John Preskill
"From this perspective, the existence of causal operations that are not localizable comes as a surprise. We seem to have the freedom to relax the rules of quantum theory by allowing more general operations, without encountering unacceptable physical consequences. Nontrivial support for this notion is provided by the semigroup property of the causal operations. It is reasonable to insist that the operations allowed at a given time ought not to depend on the previous history of the system; since the composition of two causal operations is causal, a theory that admits more general causal operations than those allowed in local quantum theory could adhere to this proviso."

 

[Demystifier]

Also it seemed to me that in your post you were hinting at some mysterious "ontological" connection between our human equations and the reality: that the description really was connected somehow with true Being---that the equations "knew more" than we do.

What I meant is the following. Sometimes, equations fit reality much better than we expected (e.g., prediction of positron by the Dirac equation). When this happens, it is hard to resist temptetation to believe that equations are somehow more clever than their inventors, and consequently, that equations are not ONLY the description, but also something "real" or "ontological".

 

[Paulibus]

...it is hard to resist temptation to believe that equations are somehow more clever than their inventors, and consequently, that equations are not ONLY the description, but also something "real" or "ontological".

A mysterious something "real"? Sounds a bit contra-eponymous to me!

I suspect that you are inclining to a belief that I've found shared by many mathematicians; that equations (and mathematics generally) are something 'found', which one discovers. I prefer to think that mathematicians spend their time inventing a clever language --- not unrelated to music and the game of chess --- and that physicists, as more pedestrian folk, carpenter away at describing discovered reality with this language. Happily it takes two to tango!

 

[Demystifier]

A mysterious something "real"? Sounds a bit contra-eponymous to me!

I suspect that you are inclining to a belief that I've found shared by many mathematicians; that equations (and mathematics generally) are something 'found', which one discovers. I prefer to think that mathematicians spend their time inventing a clever language --- not unrelated to music and the game of chess --- and that physicists, as more pedestrian folk, carpenter away at describing discovered reality with this language. Happily it takes two to tango!

So you and me have different views on the Wigner's "Unreasonable Effectiveness of Mathematics in the Natural Sciences":
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

 

[TrickyDicky]

What I meant is the following. Sometimes, equations fit reality much better than we expected (e.g., prediction of positron by the Dirac equation). When this happens, it is hard to resist temptetation to believe that equations are somehow more clever than their inventors, and consequently, that equations are not ONLY the description, but also something "real" or "ontological".

A mysterious something "real"? Sounds a bit contra-eponymous to me!

I suspect that you are inclining to a belief that I've found shared by many mathematicians; that equations (and mathematics generally) are something 'found', which one discovers. I prefer to think that mathematicians spend their time inventing a clever language --- not unrelated to music and the game of chess --- and that physicists, as more pedestrian folk, carpenter away at describing discovered reality with this language. Happily it takes two to tango!

So you and me have different views on the Wigner's "Unreasonable Effectiveness of Mathematics in the Natural Sciences":
http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

Hamming's explanations of the unreasonable effectiveness of math seem quite reasonable to me.
My own view is that as always it is tempting to evoke some mystery, that's just human nature, but it is not really hard to find examples, that are so far not contradicted by observations , of physical arrangements that dissolve any mystery wrt the effectiveness of math in physics.

Say there is a constant and uniform physical entity, call it universe (this is a quite typical assumption in physics and in science in general, think of the constancy of physical laws throughout the universe, the homogeneity assumption...).
Now this particular physical arrangement will have certain constant relationships within its elements, will follow certain particular patterns and evolution, particular properties and magnitudes that will allow to define mathematical equations that will differ from other conceivable particular physical entities.

In as much as it is possible for humans(and perhaps this is indeed a mystery) to develope a symbolic language that allows to play with relationships between elements such as mathematics, it should come as no surprise that we are able to model at least partially some of the traits of the assumed homogeneous and constant physical entity. Of course most conceivable mathematical objects will not correspond to the physical entity, but humans obviously select of all the conceivable infinite set those that are more practical in their environment which happen to be those closer to the properties of the physical entity assumed. This selection process is often unconscious which lends itself to atttribute to the math language itself some magical properties.
It follows quite easily from this that mathematical objects have no reality of their own other than how closely they resemble the properties and structure of the physical entity in case.
It is not automatic either that human ingenuity will eventually find the more fitting equations dscribing the universe, but it suggests that it is certainly possible. The only evidenc is that so far it has only found equations like the EFE, Schrodinger's, Dirac's... that give very good approximations but that aren't obviously completely correct(given their incompatibility) in the sense of modelling a single physical entity coherently, but are good enough to model it partially.

Whether the particular mathematical object "manifold" is capable of accomplishing the modelling of the universe that I refer to above or we need a different object/s as has been suggested in this thread is an interesting debate IMO.

 

[strangerep]

I feel that the "Nature is more than equations" subdiscussion is hijacking my thread.

I created a https://www.physicsforums.com/showthread.php?t=731870 where those discussions can continue, and I've asked the Mentors to move relevant posts into the new thread. Please continue that subdiscussion there instead of here.

 

[marcus]

I feel that the "Nature is more than equations" subdiscussion is hijacking my thread.

I created a https://www.physicsforums.com/showthread.php?t=731870 where those discussions can continue, and I've asked the Mentors to move relevant posts into the new thread. Please continue that subdiscussion there instead of here.

That seems like a good idea. QBism is interesting in and of itself. We could try to stay focused on QBism in this thread and let the other discussion gravitate to the other thread.
QBism is new to me and I'm not confident I understand its main thrust. Mermin seems to be a really effective advocate so I will assume it is "what Mermin says".

I liked the article very much that you linked in post #33:

Looks like N.D.Mermin is still thinking about this stuff...

N. D. Mermin,
QBism as CBism: Solving the Problem of "the Now",
Available as: http://arxiv.org/abs/1312.7825
...

He communicates the gist of CLASSICAL QBism and he uses it to solve the problem of NOW.
We are talking about aninterpretation of Quantum Mechanics that solves several problems that hound other interpretations and also has a classical correlative that solves a chronic classic irritation that festers around the "block universe" idea.

So it might be fun to quote a paragraph or two of that paper you mentioned in post #33

 

[marcus]

==quote Mermin page 2==
“Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation.”
The issue here is not that the simultaneity of two different events in different places depends on frame of reference. The issue is that physics seems to have nothing whatever to say about the local Now at a single event.⁸ This apparent silence is a puzzle even without the relativity of simultaneity. Physics, both pre- and post-relativistic, deals only with relations between one time and another. Nevertheless a local present moment — the Now — is immediately evident as such to each and every one of us. My experience of the Now is a primitive fact. It simply can’t be argued with.⁹ Sum; ergo Nunc est. How can there be no place in physics for something as obvious as that?
My Now is a special event for me as it is happening. The Now is distinguished from all the other events I have experienced by being the actual current state of affairs. I can distinguish it from earlier events (former Nows) which I merely can remember, and from…
==endquote==
He says that the trouble is caused by our making two mistakes:
==Mermin excerpts page 3 and page 4==
The problem of the Now will not be solved by discovering new physics behind that glowing point. Nor is it solved by dismissing the Now as an “illusion” or as “chauvinism of the present moment.” It is solved by identifying the mistakes that lead us to conclude, contrary to all our experience, that there is no place for the Now in our physical description of the world.
III. The mistakes
There are two mistakes. The first is our deeply ingrained unwillingness, noted above, to acknowledge that whenever anybody uses science it has a subject as well as an object. It is the well-established habit of each of us to leave ourself — the experiencing subject —completely out of the story told by physics.^12,13
The second mistake is the promotion of space-time, from a 4-dimensional diagram that we each find an extremely useful conceptual device, into what Bohr called a “real essence”. My diagram enables me to represent events from my past experience, together with my possible conjectures, deductions, or expectations for events that are not in my past, or that escaped my direct attention. By identifying my abstract diagram with an objective reality, I fool myself into regarding the diagram as a 4-dimensional arena in which my life is lived.
==endquote==
Beautiful!

And solipsism is out of the question because there are a multiplicity of observers/agents who moreover can communicate among themselves.
==Amusing footnote laughing at the solipsism charge, on page 3==
11 It is not obvious to a distinguished philosopher of science, who recently had this to say about an unpublished, unarXived talk on the Now that I gave at the Perimeter Institute in 2009 [a video is at http://pirsa.org/09090077]: “A distinguished quantum theorist insisted that the past is just a model we invent to make sense of present evidence and not to be taken literally. . . .The time snobs’ chauvinism of the present moment slides easily into solipsism.” [Huw Price, Science 341, 960-961, 30 August 2013.] The QBist (CBist) recognition that the subject in science is as important as the object often elicits charges of solipsism, even though the multiplicity of subjects (agents) and their ability to communicate with each other is a crucial and explicit part of both the general QBist story and the particular CBist application I describe here, particularly in Section V below.
==endquote==

No time to finish or edit. Have to go to supper. It is 7:25 PM Pacific.
Now I'm back. So the two (actually classical) points he wants to make are:
1. What matters is the information exchanged between two subsystems. If one happens to be called an "observer" don't discount the observer. Even a rock can have a NOW. "I am, therefore it is now." Sum, ergo nunc est
2. The 4D blocky picture is a useful conceptual device but don't let that fool you into accepting it as "ontology". BTW events are not POINTS. That's a radical idealization. Events have extension and so do clocks. And reading a clock takes time…etc etc.

I think that's what he's saying in section III. It's an entertaining lively provocative paper. I think there are some strategic ideas here that could simplify both our view of basic physics and our frustrating attempts to interpret quantum mechanics.

Mermin says he is not sure what CBism (a term he coined for the classical correlative of QBism) actually stands for! He thinks maybe it stands for "Classical Bohrism". Why not? I'm certainly good with that.

I think it is possible that there is a RIGHT interpretation of Quantum Mechanics. What a surprising idea! since we are used to a menu of them, each one inedible in its own way.


 

[strangerep]

[...Mermin quote...]
Beautiful!

Yes. I enjoy his writing style.

But I wonder about all this "personal experience of Now" stuff -- in the context of Atyy's remarks about psychological time. I don't experience an event until slightly after the signals have entered my brain and been processed far enough to register in my conscious mind. One needs some background on the pre-conscious and conscious, but the science of psychology+neurology seem still very far from a detailed model of brain->mind.

So, for purposes of physics, I retreat to the simplicity of some form of automated sensing system, recording incoming signals on (some equivalent of) a spatially sequential tape. And "ideal systems" instead of "observers". Then a notion of interaction (i.e., recorded communication) in terms of coalescence and splitting of ideal systems seems doable. E.g., a photon (ideal system 1) is absorbed by a atom (ideal system 2). Then there is only one ideal system: the atom in an excited state. Later, they probably split into 2 ideal systems again, but now they're correlated. This relates to the Mermin footnote you quoted, i.e.,

[...] the multiplicity of subjects (agents) and their ability to communicate with each other is a crucial and explicit part of both the general QBist story [...]

 

[TrickyDicky]

I feel that the "Nature is more than equations" subdiscussion is hijacking my thread.

The "subdiscussion" started in page three of "your thread" about a week ago as a comment by Demystifier on the Mermin's paper subject of the thread, and continued by Marcus and others in page 4 without you or anyone apparently considering it as hijacking. If it hadn't been for Marcus insistence on clarifying Demystifier's "Nature is more than equations" comment about Mermin's paper I don't think the "subdiscussion" would have gone further than a casual post,-on topic as it was meant as a comment on the thread's subject-.
Of course you are entitled to feel hijacked whenever you wish but it puzzles me that you didn't feel it in the previous pages of the thread.

 

[marcus]

If it hadn't been for Marcus insistence on clarifying Demystifier's "Nature is more than equations" comment about Mermin's paper I don't think the "subdiscussion" would have gone further...

My fault then. Sorry about accidentally getting us off track. Hope we can get back down to business.
I'm eager to understand more about the QB interpretation of QM.

 

[marcus]

Here's Strangerep's original post:

Just finished a first reading of this paper:

C.A.Fuchs, N.D.Mermin, R.Schack,
"An Introduction to QBism with an Application to the Locality of Quantum Mechanics",
http://arxiv.org/abs/1311.5253

Abstract:
==quote==
We give an introduction to the QBist interpretation of quantum mechanics. We note that it removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades. As an example, we show in detail how it eliminates “quantum non locality”.
==endquote==

Interesting that it has ideas that remind me of Rovelli's Relational QM and Relational EPR (which I find appealing), though Rovelli is not cited in the FMS paper.

I like it because (imho) it cuts through a lot of the widespread BS that wafts around QM.

(I mention the FMS paper here in BSTM, rather than the quantum forum, since it's a bit off the mainstream.)

So can someone summarize what the QBist interpretation of QM is and briefly say how it removes the ...pseudo-problems that have plagued quantum foundations for nine decades?

I believe it actually does do that, and am eager to get a better grasp of it.

 

[atyy]

So can someone summarize what the QBist interpretation of QM is and briefly say how it removes the ...pseudo-problems that have plagued quantum foundations for nine decades?

I believe it actually does do that, and am eager to get a better grasp of it.

I dislike all the expositions by Mermin on this topic. I do find one idea attractive in QBism. That idea is that collapse is like Bayesian updating. Bayesian coherence is a standard term in Bayesian inference. This is a very old idea that is hinted at in Cohen Tannoudji, Diu and Laloe's text, and mentioned in the recent text of Wiseman and Milburn.

Here is an example of Bayesian "coherence" in standard statistical usage: http://mlg.eng.cam.ac.uk/mlss09/mlss_slides/Jordan_1.pdf.
Are You a Bayesian or a Frequentist?
Michael I. Jordan

All solutions to the measurement problem introduce new postulates from which the Born rule or projection postulate are derived. For example, Bohmian mechanics introduces non-local hidden variables. Many-worlds introduces branching realities. Both are successful in the sense that the additional postulates are more natural.

Qbism introduces the new postulate "Principle of Reciprocity: Posteriors from Maximal Ignorance Are Priors" from which the projection postulate is derived. If you believe the new assumption is "natural", then it solves some aspect of the measurement problem.

The postulate is stated on p17 and p23 (Eq 130) of:
http://arxiv.org/abs/1301.3274
Quantum-Bayesian Coherence: The No-Nonsense Version
Christopher A. Fuchs, Ruediger Schack
Rev. Mod. Phys. 85, 1693–1715

For comparison, here's the different but related approach of Leifer and Spekkens, which I like:
http://arxiv.org/abs/1107.5849
Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
M. S. Leifer, R. W. Spekkens

Leifer and Spekkens compare their approach with QBism:
"It follows that in the conditional states framework, the steering effect is merely belief propagation (updating beliefs about one system based on new evidence about another) and does not require any causal influence from one to the other. This interpretation has been advocated previously by Fuchs [22]."

"By contrast, our work takes quantum states to represent the beliefs of an agent about a spatio-temporal region and takes quantum operations to represent belief propagation; it has an epistemological flavor rather than an operational one. For instance, the notions that we deem to be most promising for making sense of the quantum formalism are those one finds in textbooks on statistics and inductive inference, such as Bayes’ theorem, conditional probabilities, statistical independence, conditional independence, and sufficient statistics and not the notions that are common to the operational approaches, such as measurements, transformations and preparations. In this sense, our approach is more closely aligned in its philosophical starting point with quantum Bayesianism, the view developed by Caves, Fuchs and Schack"

"Unlike the quantum Bayesians, however, we are not committed to the notion that the beliefs represented by quantum states concern the outcomes of future experiments. Rather, the picture we have in mind is of the quantum state for a region representing beliefs about the physical state of the region, even though we do not yet have a model to propose for the underlying physical states."

Of relevance to whether hidden variables are consistent with an "epistemic" approach are papers that support the existence of psi-epistemic hidden variables:

http://arxiv.org/abs/1201.6554
Distinct Quantum States Can Be Compatible with a Single State of Reality
Peter G. Lewis, David Jennings, Jonathan Barrett, Terry Rudolph

http://arxiv.org/abs/1303.2834
Psi-Epistemic Theories: The Role of Symmetry
Scott Aaronson, Adam Bouland, Lynn Chua, George Lowther

There is a proof that maximally psi-epistemic hidden variables are forbidden:
http://arxiv.org/abs/1207.6906
How statistical are quantum states?
O. J. E. Maroney

 

[marcus]

I dislike all the expositions by Mermin on this topic. I do find one idea attractive in QBism. That idea is that collapse is like Bayesian updating...

I recall that the "updating" idea arose our discussion of the Rovelli Smerlak paper some time ago. Each observer has his own Hilbertspace to keep track of his information and updating is not something catastrophic that the world does, it is just something he does in his own file system to stay au courant.

You are on a different schedule from me, Atyy. You already understand QB interpretation and are starting to critique it and consider antecedents alternatives and improvements. I basically want to understand better, especially what Mermin is saying.

We have these two recent papers that Rep mentioned:
November FMS http://arxiv.org/abs/1311.5253
December Mermin http://arxiv.org/abs/1312.7825
That defines what QB is, for me, and what I want to concentrate on.

When Mermin talks about probability he refers to Bruno de Finetti:
[[That probabilities are personal judgments was put most forcibly by Bruno de Finetti, and if “B” has to stand for anything I would expand “QBism” to “Quantum Brunoism.”]]
I believe in this case it is the personal judgements of a rational bettor. What wagers would an ideal rational Bookie consider fair? He mentions is the concept of a "Dutch Book" which I suspect is where a good bookie writes down the odds at which to buy and sell bets.

 

[atyy]

I recall that the "updating" idea arose our discussion of the Rovelli Smerlak paper some time ago. Each observer has his own Hilbertspace to keep track of his information and updating is not something catastrophic that the world does, it is just something he does in his own file system to stay au courant.

You are on a different schedule from me, Atyy. You already understand QB interpretation and are starting to critique it and consider antecedents alternatives and improvements. I basically want to understand better, especially what Mermin is saying.

We have these two recent papers that Rep mentioned:
November FMS http://arxiv.org/abs/1311.5253
December Mermin http://arxiv.org/abs/1312.7825
That defines what QB is, for me, and what I want to concentrate on.

When Mermin talks about probability he refers to Bruno de Finetti:
[[That probabilities are personal judgments was put most forcibly by Bruno de Finetti, and if “B” has to stand for anything I would expand “QBism” to “Quantum Brunoism.”]]
I believe in this case it is the personal judgements of a rational bettor. What wagers would an ideal rational Bookie consider fair? He mentions is the concept of a "Dutch Book" which I suspect is where a good bookie writes down the odds at which to buy and sell bets.

No, if you read my post #89 it is my summary of QBism you asked for. I simply dislike Mermin's writing about it. I believe the review by Fuchs and Schack I linked to is a far better exposition of QBism. The statistical method of Bayesian inference I mentioned is based in large part on de Finetti's work, and the formal notion of Bayesian coherence I mentioned is de Finetti's. The Dutch Book example is a famous example illustrating Bayesian coherence.

 

[Dale]

It has been recommended that we close all the threads about QM interpretations in order to be coherent with the closure of the spawned thread.